Question

Simplify the expression. 3 + 4i over 2 + 4i

Answer 1

`(3+4i)/(2+4i)=(3+4i)/(2+4i)\cdot(2-4i)/(2-4i)=((3)(2)+(3)(-4i)+(4i)(2)+(4i)(-4i))/(2^2-(4i)^2)\\\\=(6-12i+8i-16i^2)/(4-16i^2)=(6-4i-16(-1))/(4-16(-1))=(6-4i+16)/(4+16)\\\\=(22-4i)/(20)=\boxed{(11-2i)/(10)}=\boxed{(11)/(10)-(1)/(5)i}`